168 CHEMICAL ENGINEERING The opening of the discharge is effected by means of vertically placed poppet valves. At the end of each stroke, however, the discharge is mechanically closed by means of a Corliss semi-rotary valve directly under the poppet valves, thus retaining under the latter a cushion of air under discharge pressure, enabling them to seat without violent and noisy impact. The construction is such that very small clearances are possible. In a 28 X 30-in. cylinder, for example, it is but 0.7 per cent. This type of gear has proved very successful on dry air pumps when very high vacuum is required. AIR COMPRESSION Theory of Air Compression.—If it be assumed that a compressor works under ideal conditions without clearance and without friction losses and the compression from p\ to pz (Fig. 26) follows the law pv» = K7 the work done is W = n (p*v2 - Pivi)/(n - 1) = npa)i [(p2/pi)(n~1)/n - l]/n - 1). The temperature at the end of the compression is given by T^/Ti = p2/pi(ri~"1)/?l. The work W .1 FIG. 26. O 3' Air-compressor cycle. FIG. 26a. decreases as n decreases and to decrease n from its adiabatic maximum (n = 7 = 1.406 approximately) is the function of the water jacket (or the petticoats on the cylinder, if air-cooled). When the pressure pz is high it is advantageous to divide the process into two or more stages and cool between the cylinders. The saving is best shown on the temperature-entropy diagram (Fig. 26a). With single-stage compression, 12 represents the compression from pi to p%, and if the constant-pressure line 23 is drawn cutting • the isothermal through point 1 in point 3, the area 1' 1233' represents the work W. When two stages are used, 14 represents the compression from pi to an intermediate pressure p', 45 cooling at constant pressure in the intercooler between the cylinders, and 56 the compression in the second stage. The area under 14563 represents the total work in the two stages and 24:56 the saving due to compounding. The saving is at a maximum when T± = TQ, which is the case when the intermediate pressure p' = Vpip2- The total work in two-stage compression is npivi[(pl/pi)^n ~ V/n +(p2/p') (n - i)/» __ 2] /n-l. Mean Effective Pressure in Multi-stage Compression.—The mean effective pressure, pounds per square inch, with complete intercooling, referred to the l.-p. piston, is expressed by the formula where S represents the number of stages and n is the exponent of the compression curve. Figure 27, from a chart plotted by F. W. O'Neill, shows the relation between the mean